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#379×C₁₃₉ #22580464

order	8896
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃₉ · Schur multiplier (H₂) = C₂⁶

Aliases

#379×C₁₃₉

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂³
commutator	C₂²	C₂²×C₄×C₁₃₉
Frattini, cosocle	C₂³	C₂³×C₁₃₉
prime radical	C₂⁵×C₁₃₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

506 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3892 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₁₃₉⋊#1304, #31804332, #31806318, …
maximal subgroup of	#1304×C₁₃₉, #1316×C₁₃₉, #1781×C₁₃₉, …
maximal normal subgroup of	#1304×C₁₃₉, #1316×C₁₃₉, #1781×C₁₃₉, …
maximal quotient of	C₂²⋊#95×C₁₃₉, #1438×C₁₃₉, #1446×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 60);